The transverse and longitudinal gluon propagators in the Landau gauge are studied in the two-color lattice QCD at nonzero quark chemical potential $mu_q$. Parameterization of the momentum dependence of the propagators is provided for all values of chemical potential under study. We find that the longitudinal propagator is infrared suppressed at nonzero $mu_q$ with suppression increasing with increasing $mu_q$. The transverse propagator dependence on $mu_q$ was found to be opposite: it is enhanced at large $mu_q$. It is found, respectively, that the electric screening mass is increasing while the magnetic screening mass is decreasing with increasing $mu_q$. Nice agreement between the electric screening mass computed from the longitudinal propagator and the Debye mass computed earlier from the singlet static quark-antiquark potential was found. We discuss how the dependence of the propagators on the chemical potential correlates with the respective dependence of the string tension. Additionally, we consider the difference between two propagators as a function of the momentum and make interesting observations.
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